Structural, magnetic, and powder and single-crystal electron paramagnetic resonance (EPR) studies were performed on [{Cu(bipy)(en)}{Cu(bipy)(H2O)}{VO3}(4)](n) (bipy = 2,2'-bipyridine, en = ethylenediamine), which is a new copper-vanadium hybrid organic-inorganic compound containing Cu-II and V-V centers. The oxovanadium units provide an anionic scaffolding to the structure, where two types of Cu-II coordination modes, octahedral (Cu1) and square pyramidal (Cu2), contribute to the magnetic properties. The crystal structure contains layers including Cu1 and Cu2 ions, separated by stacked arrangements of 2,2'-bipyridine molecules. Each type of Cu-II ion in these layers forms parallel spin chains described by exchange coupling parameters J(1) and J(2) for Cu1 and Cu2, respectively (exchange couplings defined as H-ex(i, j) = -J(ij) SiSj), which, for necessity, are assumed to be equal to J. These chains are coupled by much weaker Cu1-Cu2 exchange interactions J(3) connecting neighbor Cu1 and Cu2 ions within a layer, through paths acting as rungs of a ladder chain structure. The average coupling J, which is antiferromagnetic (J < 0), according to the susceptibility data, is estimated with similar results with a mean field approximation (J = -1.4 cm(-1)), and with a uniform chain model (J = 1.7 cm(-1)). The EPR spectra of powdered samples and oriented single crystals are shown to be independent of J(1) and J(2), but are dependent on the weak coupling J(3), and the data allow a lower limit to be established: vertical bar J(3)vertical bar > 0.04 cm(-1). The spectra are also strongly sensitive to extremely weak coupling interactions with average magnitude J(4) between copper atoms in neighboring layers, separated by similar to 10 angstrom, using the stacked 2,2'-bipyridine molecules, which produce a 2D-to-3D quantum phase transition. This is observed in single-crystal samples when the energy levels are changed with the orientation of the magnetic field. From the characteristics of these transitions, we estimate a value of vertical bar J(4)vertical bar = 0.0034 +/- 0.0004 cm(-1) between Cu-II ions in neighboring layers. This work emphasizes the important possibilities of EPR to evaluate extremely small exchange couplings between metal ions in a solid material, even in the presence of other much larger couplings.